As we've seen, Eq. (7.33) describes the beat pattern. Let's now derive a different...

As we've seen, Eq. (7.33) describes the beat pattern. Let's now derive a different version of that expression assuming that the two overlapping equal-amplitude cosine waves have angular spatial frequencies of kc.+ Δk and kc- Δk, and angular temporal frequencies of ωc,.+ Δω and ωc- Δω, respectively. Here kc and ωc. correspond to the central frequencies. Show that the resultant wave is then

E=2E01 cos (Δkx - ωt) cos (kcx -ωct)

Explain how each term relates back to

Prove that the speed of the envelope, which is the wavelength of the envelope divided by the period of the envelope, equals the group velocity, namely, Δω/Δk.